### Representations and approximations of hyperbolicity cones

- Series
- Algebra Seminar
- Time
- Monday, August 20, 2012 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Daniel Plaumann – University of Konstanz

Hyperbolic polynomials are real polynomials that can be thought of as
generalized determinants. Each such polynomial determines a convex cone,
the hyperbolicity cone. It is an open problem whether every
hyperbolicity cone can be realized as a linear slice of the cone of psd
matrices. We discuss the state of the art on this problem and describe
an inner approximation for a hyperbolicity cone via a sums of squares
relaxation that becomes exact if the hyperbolic polynomial possesses a
symmetric determinantal representation. (Based on work in progress with
Cynthia Vinzant)